The latest budget deal in Washington teaches at least one lesson about a key virtue of constitutional democracy: To balance conflicting ideas, elected leaders must first build up trust between a small group of people who can then come up with a moderate agreement that tempers the excesses of each side.

That lesson has been elusive in the American capital. For years, politicians have sought a “grand bargain” that would trade tax increases for entitlement cuts. When the brinkmanship of hardened ideologies finally led to a long government shutdown in October, wiser heads looked to two lesser-known leaders of Congress, Rep. Paul Ryan (R) of Wisconsin and Sen. Patty Murray (D) of Washington State. The two budget chairs set about quietly finding a modest middle ground that would fund the federal government for the next two fiscal years.

The details of their agreement matter less than the political lesson: Government must be restructured to force leaders to negotiate with trust, seek incremental progress, and weave differing values into a compromise for the common good.

Americans should not expect much restructuring from Washington anytime soon, however. Its political class of incumbents thrives on gerrymandered districts, primaries that rely on ideological voters, and powerful, monied special interests. Rather, smaller levels of government must create new ways to push politicians into negotiating with the virtues similar to those that led to the Ryan-Murray deal.

A few states have taken the process of redistricting legislative seats every 10 years out of the hands of elected leaders and given the responsibility to independent groups. Others have restrained the level of money in politics. But perhaps the most interesting experiment lies in new ways to hold state-run primaries.

California, Washington, and, to a degree, Louisiana, have primary elections in which voters can select a candidate of any party on the ballot. The top two primary winners – no matter what their party – then face off in the general election. In many cases, the final vote pits a liberal Democrat against a conservative Democrat, or a conservative Republican against a liberal Republican.

This “top two” method can have one big effect: It pushes candidates to appeal to independents and the moderates of an opposing party. Any party dominated by narrow interests may not do well.

Once in office, a politician who seeks reelection would be more willing to forge coalitions across party lines, hoping to define a middle ground through give-and-take rather than play to a small wing of a party with disproportional influence in a primary.

In California, which began using “top two” primaries in 2012, the effect of the new system has been most noticeable. The state has had 28 races in which the top two candidates were of the same party. And many incumbents either lost or decided not to run.

Nonpartisan election primaries are not perfect. Wealthy candidates might tend to dominate. Small parties built around a single issue would not do well. Voters would need to do their homework on candidates rather than “vote the party.” Some analysts prefer that the top four instead of top two vote-getters in an open primary be allowed to run in the general election.

Still, states need to start fixing American politics piece by piece. They serve as laboratories for experiments in different styles of governance.

For elected leaders, reaching across party lines can sometimes require a compromise of ideology but not necessarily of principles. As analyst George Friedman of the Stratfor think tank recently wrote:

“There is a vast difference between principle and ideology. Principles are core values that do not dictate every action on every subject, but guide you in some way. Ideology as an explanation of how the world works is comprehensive and compelling. Most presidents find that governing requires principles, but won’t allow ideology. But it is the senators and particularly the congressmen – who run in districts where perhaps 20 percent of eligible voters vote in primaries, most of them ideologues – who are forced away from principle and toward ideology.”

The Ryan-Murray deal was achieved in that spirit of principled compromise. But it is in the states now experimenting with new political structures that may eventually lead Washington to change its ways.